Q.State the quadrant, or the axis, in which each of the following points lies:

This is a direct application of the quadrant sign convention — read off the sign of the abscissa and the ordinate of each point and match it against the table for Quadrants I–IV, remembering that a zero coordinate means the point lies on an axis instead.

1. $(5,-2)$: $x>0, y<0 \Rightarrow$ Quadrant IV.
2. $(-3,-7)$: $x<0, y<0 \Rightarrow$ Quadrant III.
3. $(0,4)$: $x=0 \Rightarrow$ on the y-axis (above the origin).
4. $(-6,3)$: $x<0, y>0 \Rightarrow$ Quadrant II.
   ✓Final answer

   (i) Quadrant IV (ii) Quadrant III (iii) on the y-axis (iv) Quadrant II

Every point's quadrant (or axis) can be read directly from the sign of its abscissa $x$ and ordinate $y$, using the Quadrant Sign Convention: $(+,+)\to$ I, $(-,+)\to$ II, $(-,-)\to$ III, $(+,-)\to$ IV; and $x=0$ places the point on the y-axis while $y=0$ places it on the x-axis.

(i) $(5, -2)$: here $x=5>0$ and $y=-2<0$, so the signs are $(+,-)$, which is Quadrant IV.

(ii) $(-3, -7)$: here $x=-3<0$ and $y=-7<0$, so the signs are $(-,-)$, which is Quadrant III.

(iii) $(0, 4)$: here $x=0$, so this point does not lie inside any quadrant — it lies exactly on the y-axis, and since $y=4>0$ it lies above the origin, on the positive y-axis.

(iv) $(-6, 3)$: here $x=-6<0$ and $y=3>0$, so the signs are $(-,+)$, which is Quadrant II.

Students often confuse the numbering direction of the quadrants (mixing up II and IV) or forget that a point with one coordinate equal to zero does not lie in any quadrant at all — it lies exactly on an axis, which is a separate case from all four quadrants.